Lyman;
The manufacturer writes the AOM but the airlines are free to modify according to their own requirements, obviously within reason. The modification I believe must be approved by the manufacturer and the country's regulator... someone?
Under the heading that anything is possible, positing an unbelted pilot remains in the "extremely unlikely" category in which everything is possible but without the capacity to enhance understanding.
If the PF had let go the stick the airplane likely would have gently, slowly recovered on its own, not, perhaps before impact but it may have silenced the stall warning, got the airspeed indicators working again, (because they had recovered by the time the airplane started down, post-apogee), and reduced confusion. It was the mostly-NU stick that held the airplane in the stall.
I view the BEA remark as nothing more than an investigative observation of fact.